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The Quantum Mechanics Solver 22

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For large ωt, the amplitude is the same for all sites of the same parity:. The edges of the region where the probability is non zero propagate in opposite directions with the velocity v = πωa/2. A Quantum Box. A quantum box is made of a material A on which another material B is deposited. The side of the square...

The Quantum Mechanics Solver 23

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correspond to the degeneracy of an energy level of ˆ H 0 found previously. If two different states would correspond to the same couple of eigenvalues (n l , n r. the corresponding point of the diagram would be twofold degenerate, and the degeneracy of the energy level E N would be larger than N + 1.. We must find...

The Quantum Mechanics Solver 24

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One also obtains λ N A, which absorbs red light and gives a green color to the corresponding pigment. Note that the presence of the nitrogen atom yields λ N 13 ≤ λ N 11 whereas λ 0 13 >. Consequently, if a wave function has a node at the center, it has an antinode in the vicinity of the...

The Quantum Mechanics Solver 25

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24.1 Muonium in Vacuum. This atom falls into its ground state very quickly (in ∼ 10 − 9 s), the muon’s spin state remaining the same during this process. We assume that, at t = 0, the state of the muonium atom is the following:. The muon spin is in the eigenstate. The wave fuction Ψ ( r ) of...

The Quantum Mechanics Solver 26

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The oscillations of the surface of the liquid are studied in Sect. At what distance from the surface does gravity become larger than the Van der Waals force? In what follows, we shall neglect the gravitational force.. Show that the eigenstates of the Hamiltonian which describes the motion of the H atom are of the form |k. φ σ ,...

The Quantum Mechanics Solver 27

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Laser Cooling and Trapping. We then show that the cooled atoms can be confined in the potential well created by a focused laser beam.. (26.1) where d , which is assumed to be real, represents the matrix element of the atomic electric dipole operator between the states | g and | e (i.e. In all the chapter we assume that...